Dynamics of the detonation-wave front in solid explosives

The important role of the shape of the front during detonation wave propagation in gas mixtures was substantiated by K. I. Shchelkin during construction of the theory of spinning detonation. Subsequently, a unique relationship between the curvature of the front and detonation wave parameters has been repeatedly confirmed in experiments, including for condensed high explosives (HEs). The existence of this relationship formed the basis of the theory of the dynamics of the detonation front which had been developed by the end of the 20th century. This paper presents the results of a study of detonation front propagation in cylindrical samples of a low-sensitivity HE of different diameters with one-point and plane-wave initiation. A unique relationship between the detonation velocity and the curvature of the detonation wave front has been found. Ordinary differential equations describing two-dimensional steady-state detonation front profiles for HE charges in the form of a plate, a cylinder, and a ring were derived assuming that the detonation velocity depends on the curvature of the front. It was taken into account that the boundary angle between the normal to the front and the HE edge is unique for each combination of HE and liner material. It was found that the same detonation front profile corresponds to several combinations of liner material and the determining size of the charge (plate thickness, radius of the cylinder or the inner radius of the ring). A comparison of experimental front profiles near the edges of HE charges for these combinations provides data on the dependence of detonation velocity on the curvature of the front at low velocities corresponding to shock-induced detonation regimes. Analysis of previously obtained data for detonating ring charges of low-sensitivity HEs shows that as the detonation velocity decreases, the total front curvature tends to a limit of about 0.05 mm$^{-1}$, i.e., of the order of the inverse critical diameter. The limit of the front curvature allows predicting the critical detonation diameter.